Basics of Programming:
if…else, iterations,
custom functions

Enrico Toffalini

Conditional Programming

Conditional statements like if, if...else, and ifelse in R are essential tools for automating tasks and assisting decision making in data science. What follows are a few simple “toy examples”, but focus on the underlying logic. This will be greatly useful in more advanced applications

if statement

the if statement performs an action only if a condition is met 
age = 20
if(age >= 18){
  print("Adult")
}
[1] "Adult"

if statement

Basic flowchart showing the logic of the if statement:

if...else statement

Sometimes, however, you may need to perform alternative actions

if...else statement

Sometimes, however, you may need to perform alternative actions

Here is a practical example of the if...else statement 
age = 15
if(age >= 18){
  print("Adult")
} else {
  print("Minor")
}
[1] "Minor"

In the above example:

  • if age is 18 or older, R will print "Adult";
  • otherwise (else) it will print "Minor"

if...else if...else statement

When you need to evaluate more than just two alternative conditions, you can use nested conditional statements, that is you combine multiple if...else statements 
age = 10
if (age >= 18) {
  print("Adult")
} else if (age >= 13) {
  print("Adolescent")
} else if (age >= 2){
  print("Child")
} else {
  print("Infant")
}
[1] "Child"

if...else statement

Possible, pratical use of if...else in a preplanned analysis for a hypothetical preregistered study: automate the decision to conduct additional analyses based on the result of a preliminary test. This helps create a reproducible analysis pipeline with a clear set of decisions

## PREPLANNED ANALYSIS

# preliminary test
tt1 = t.test(x1, x2, data=df, paired=TRUE)

# based on the p-value of the preliminary t-test, choose the next step
if (tt1$p.value < 0.05) {
  # If significant, perform an additional analysis with a linear model (lm)
  print("Significant result: proceeding with follow-up analysis")
  fit = lm(outcome ~ pred1 + pred2 * moder1, data = df)
  summary(fit)
} else {
  # else, report only the preliminary test
  print("No significant result: reporting preliminary results only")
  print(tt1)
}

if...else statement

All previous examples required to evaluate a single particular condition that might be TRUE or FALSE. However, you often want to apply this type of operation to an entire vector

Using if and if..else directly on a vector will NOT work as intended:

age = c(2, 28, 15, 1, 4, 67, 42, 14, 7)

if(age >= 18){
  print("Adult")
} else {
  print("Minor")
}
Error in if (age >= 18) {: the condition has length > 1

ifelse()

All previous examples required to evaluate a single particular condition that might be TRUE or FALSE. However, you often want to apply this type of operation to an entire vector

To handle such cases you can use the base ifelse() function, that evaluates each element of a vector individually:

age = c(2, 28, 15, 1, 4, 67, 42, 14, 7)

ifelse(age >= 18, "Adult", "Minor")
[1] "Minor" "Adult" "Minor" "Minor" "Minor" "Adult" "Adult" "Minor" "Minor"

— Best practices: store results and set type as appropriate!

ageCategory = ifelse(age >= 18, "Adult", "Minor")
ageCategory = factor(ageCategory, levels=c("Minor", "Adult"))
ageCategory
[1] Minor Adult Minor Minor Minor Adult Adult Minor Minor
Levels: Minor Adult

ifelse()

The ifelse() function can also be nested to manage multiple conditions, such as in the following example:

age = c(2, 28, 15, 1, 4, 67, 42, 14, 7)

ifelse(age >= 18, "Adult" , 
               ifelse(age >= 13, "Adolescent" ,
                            ifelse(age >= 2, "Child", 
                                                 "Infant")))
[1] "Child"      "Adult"      "Adolescent" "Infant"     "Child"     
[6] "Adult"      "Adult"      "Adolescent" "Child"

dplyr::case_when()

While this works, the nested structure can become cumbersome as the number of conditions increases.

The above case may become cumbersome and less readable when you need to combine a large number of conditions. In such cases, the case_when() function from the dplyr package (part of the tidyverse collection)

age = c(2, 28, 15, 1, 4, 67, 42, 14, 7)

library(dplyr)

case_when(
  age >= 18 ~ "Adult",
  age >= 13 ~ "Adolescent",
  age >= 2  ~ "Child",
  TRUE      ~ "Infant"
)
[1] "Child"      "Adult"      "Adolescent" "Infant"     "Child"     
[6] "Adult"      "Adult"      "Adolescent" "Child"

Iterative Programming

Iterative programming allows you to repeat one or a series of actions automatically, for a predetermined number of times or until a condition is met

Let’s start with understanding the basics of iterative programming with the for loop:

for loop

Here are a few simple examples of using the for loop 
for(i in 1:5){
  print(i)
}
[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
for(i in 1:5){
  print(i^2)
}
[1] 1
[1] 4
[1] 9
[1] 16
[1] 25
for(i in 1:5){
  print(Sys.time())
  Sys.sleep(1)
}
[1] "2024-11-23 14:46:26 CET"
[1] "2024-11-23 14:46:27 CET"
[1] "2024-11-23 14:46:28 CET"
[1] "2024-11-23 14:46:29 CET"
[1] "2024-11-23 14:46:30 CET"
for(i in 1:5){
  print(Sys.time())
  Sys.sleep(2)
}
[1] "2024-11-23 14:46:31 CET"
[1] "2024-11-23 14:46:33 CET"
[1] "2024-11-23 14:46:35 CET"
[1] "2024-11-23 14:46:37 CET"
[1] "2024-11-23 14:46:39 CET"

for loop

Here’s a more interesting example of iterative for loop with practical usefulness: we want to repeat a data simulation for a predetermined number of times (5 iterations), each time drawing \(n = 30\) values from a standard normal distribution, computing and displaying the average …

set.seed(0) # set a seed for reproducibility: best practice! 

for(i in 1:5){
  x = rnorm(n = 30, mean = 0, sd = 1)
  print(mean(x))
}
[1] 0.02195079
[1] -0.02577153
[1] -0.009581231
[1] 0.03212316
[1] -0.2946441

This is actually the starting point of a Monte Carlo simulation! 😃

for loop

in the previous example, the for loop displayed the results but didn’t store it. For more effective use, you can combine the for loop with indexing with [] to save each result:

set.seed(0) # set a seed for reproducibility: best practice! 
niter = 5 # set the desired number of iterations: best practice! 
# initialize a results vector with NAs: best practice!
results = rep(NA, niter) 
# now run the for loop! :-)
for(i in 1:niter){
  x = rnorm(n = 30, mean = 0, sd = 1)
  results[i] = mean(x)
}
results # display results
[1]  0.021950789 -0.025771530 -0.009581231  0.032123159 -0.294644080
sd(results) # estimate standard error of the mean
[1] 0.1358843

for loop

Let’s extend the previous example with … a few more iterations! 
# STEP 1: RUN SIMULATION

# set number of iterations
niter = 10000
# initialize results vector
results = rep(NA, niter) 
# actually run simulation
for(i in 1:niter){
  x = rnorm(n = 30, mean = 0, sd = 1)
  results[i] = mean(x)
}
# STEP 2: PLOT RESULTS

# histogram, with a large number of bins
hist(results, breaks=50) 

# STEP 3: COMPUTE SD OF RESULTS
sd(results)
[1] 0.1806616

→ Enjoy it! This is a proper estimation of the Standard Error of the Mean via Monte Carlo simulation! 😊

for loop

You don’t necessarily have to iterate over a sequence of integers (e.g., “i in 1:10000”; “j in 1:ncol(df)”), although this is the most common practice. You could iterate over whatever, for example, directly over the elements of a vector or other data structures

myVect = c("this", "is", "a", "vector", "of", "strings")

for(x in myVect){
  print(toupper(x))
}
[1] "THIS"
[1] "IS"
[1] "A"
[1] "VECTOR"
[1] "OF"
[1] "STRINGS"

while loop

The while loop is another type of iterative structure in R. It may be useful when the precise number of iterations is not predetermined, but depends on a target being reached

amount = 1000
month = 0
interest_rate = 0.001 # 0.1% monthly interest rate

while(amount < 1500){
  month = month + 1
  amount = amount + amount * interest_rate
}

month
[1] 406

Interpretation: it takes 406 months to reach an amount of \(€1,500\) when starting with an amount of \(€1,000\) with a \(0.1\)% monthly interest rate

repeat loop

The repeat loop has a logic similar to the while loop but 1) it always runs at least one iteration, 2) It explicitly emphasizes repetition until a condition (not necessarily a target) is met, using a break statement to terminate

repeat{
  roll_die = sample(1:6, 1)
  print(roll_die)
  if(roll_die == 6) break
}
[1] 2
[1] 3
[1] 1
[1] 3
[1] 1
[1] 1
[1] 5
[1] 6
attemptedExper = 0

repeat{
  attemptedExper = attemptedExper + 1
  tt = t.test(rnorm(10),rnorm(10))
  if(tt$p.value < 0.05) break
}

# number of experiments I attempted to... 
# get a false positive :-)
attemptedExper
[1] 12
round( tt$p.value , 3 )
[1] 0.041

apply family

apply is a family of base functions that provide efficient tools for running iterations on structures like dataframes, vectors, matrices, lists

Traditional loops provide a straghtforward, intuitive way to compute sequences of operations, but the apply family allows you to run faster computations… this may become particularly important when you need to parallelize for computationally intensive tasks

The following is not a computationally heavy task — but for example, let’s say we want to compute the mean value per column in this dataframe:

    BD SI DS PCn CD VC LN MR CO SS
1   13 10  7  10 15  7 10 16  8 13
2    7 11  6   8 13 10  9  5  9 14
3   12  6  5   7  9  7  7  6  9  8
4    8  7  9  11  1  5  7  6  8  4
5   12 13  8  10 10 10  9 11 13 12
6   13 17 13   7 10 19 13 10 15 13
7   12 10  9   5 10  8  7  9 11 11
8    9 12 15  14  7 11 14 13  8 14
9   11 14  8  11  8 12 14 12 10  9
10  13 12 14  11  5 15 17 14 14  8
11   7  7  7   6  6  6  4  7 12  9
12  10 11  8   8 10  7  7  8  8 15
13   5  6  4   6  7  4  7  4  4  6
14  13 14 11  12 13 17 13 12 15 13
15  10 12 11   4  5 10  7 10 13  7
16   8  8 11  10 11  9 11  5 10  8
17  10  6  7  11 11  8  9 10  9 10
18  11 12 11   7 14 16 12 15 10 15
19  10 10  6  12  9  4  9  7 13  6
20  13 10 13   8 10 10 12 13  3  9
21  16 16 16  10 15 13 14 11 14 15
22   9  8 15  12 13 11 14  9 10 11
23   4  9 14   7 13  4  9 10  4 11
24  11  6 11  12 16  8 12 11  8 17
25   8 12 10   5 14 11  9 11 11 10
26  11 15 15  16 13 11 13 12 15 13
27   9  4 10   8  9  5  9  7 11  7
28  10 14  9  12 12 18 12 12 12  8
29  10  5  6   7 10  9 10 12  7  7
30  10 10  8   9  9 11 12 13 10  8
31   9  7  7   9 10  9 12 13  8 11
32   3  7  8  11  1  5  6  8  6  8
33  10 12  9  13 10 13  9 10 15  9
34  12 13 12  12  9 11 10 10 10 13
35   8  9 10   8  8  9 13  9  6 13
36   8  6  6   5  8  7  7  9  5 10
37   4  5 11   9  8  6 11  9  5  7
38  13 11 10  10 11 10 10  9  9 12
39   8  8 13   6 16 12  8 11  7 15
40   9  9 11  10 10  6 10 11 10 12
41   5 10  8   8  9  9  8  8 11 12
42   8  6  7   6  4  6 11 12  5  7
43  12  8 12   9 11 12 10 10  8 10
44  10 10 12   9 11 15  9 10 14 11
45  10  9  7   8 11  6 10 10  7 10
46  12 10 11   8  9  7 14  9 10 12
47   8 11 10  11 10  9  9 13  4 12
48  11 12  7  11  9  8  8  9 11 11
49   7 12  9  14 16 12 13  9 11 17
50   9  9  7   9 14 13  9 11  9  9
51  11 15  6   7  7 11  5 12  8  8
52  15  7 12  10 11  7  9  8 11 12
53   7  2  3   3  6  3  1  5  1  9
54   5  8  6   7  6 10  8  8 10  6
55   9 14 14  11  8  9 12 15  9 11
56  11 10 12  13 17 11 13 10 12 10
57  11 11  9  10  7 13 13 11 12  9
58   9  9 11   4 12 12  9 11 12  6
59   9  4  8   6 11  2  9  6  7 12
60  11 10 11   8  8 12  8  6  9  6
61   7  7  7   8 11 10  8  4 10  5
62  11 13 14  10 12 14 14 13 14  8
63   6 10  9   9  8  8  6 11  9  8
64   9 11  7   8 13 10  7 11  9  9
65  13  7 12  13 13  7 10 10  9 10
66  10 13 16  15 10 15 11 12  6 15
67  14 11 11  10  7 14 12  9  9 12
68   7 11 10  10  9 11  6 11  7  8
69   6  5 12  11 13  8 14 11  6  9
70   4 10  9  14 12  9  7  9  8  6
71  13  9  4   9  7  8  8  7  9  7
72  11 12 12  10  8 10 10 10 12  6
73  11 14 10  11  9 12  8  7 16 10
74   6 NA  8   6  1 11 NA  7 12  7
75   8 11 12  11  7 13 12  7 15 12
76  10  9 11  13 12 11 14 10 12 10
77  10  2  5   5 11  5  6  2  6  7
78   8  6  9   8  6  9 11  5  7  6
79   6  3  5   8  6  8  5  8  6  7
80  10  7 10  11  9 11  6 11  9  9
81   6  9  6   7 13  7 15  9 11 13
82  11  8 11  10 11 14  6 11 14 10
83  12 15 11  12 11 11 13 12 12 10
84   7  7  8  12 14  9  5  6  6 12
85   9 12 10  10  5 13  8 11 15  8
86  14  9 10  11 13  7  8  8  7 10
87  14  8  6  NA  9  5  5  9  9  9
88  15 11  9  11 11 12  9 12 10  9
89  11  9 16  13 11 13 16 14 10 12
90  10  7 13   8 13  7 13  6  9 13
91  14  9 11   8 NA 10 10 12  8 10
92  13  6  8   7 11  9  4 13 12 10
93  10  9  7   9  7  8 10 11  9  6
94  12  6  8  10  5  4  8 10  5  5
95  17 12 14  17 14 16 11 18 14  9
96  11 NA 11  12  8 13 11 12  9 10
97   8 12 14   7 10 10 11 10  9 12
98  13 13  7  11 12 13 11 12 13 10
99   8 10  8   9 10  9  9  8 14  8
100  7  6  3   6 14  6  6  9 10 11
101  7  9  8   9 10  9 10  7  7  6
102 11  9 12  10 10  9 11 11  9  9
103 11 11 13  10 10 11  8  8 10  9
104  9 14 12  12  5 12  9  9 13 10
105  5  3  7   7  7  3  4  7  7  8
106  9  9  9  11 14  7  9 11  9 13
107  9 12  7  15  6 13  8 10 12 10
108 12  9 14   8 13 10 14 13 13  9
109  9  8  8   6  9  7  9  8  9 NA
110  7 15 12  11 14 13 14 10 13 11
111 11 13 10  10  9  9 13 13  8 10
112  9  8  8  15  8 14 13 12 11 10
113 12  8  7  12 10 10 11  6 10 10
114 11 12 14  10  8 13 13 10  8 13
115 10 13  9  10 11 15 11 11 10 14
116 10  4  4   5 11  1 10  9  6 10
117  7  8 12   5 10  5  7  8 11  8
118 10  7  3  11 10  6  7  8  7  8
119 11 11  7  10 14  9  9 10 13 12
120 11 15 11  11  6 14 15 13 15  8
121  7 10 11  10  8 11  9  7 10 10
122  9 10 13   9  7  7 11  6 11  9
123  6  8 12   8  9 10 10  9  6  7
124 13  8  8   5 11  8 16  9 16 10
125 10  8  6   7  8  9  9  8  6 10
126  3  7  7   7  7  8 10  6  9  6
127  5  9 13   9  9  7  6  6  8 10
128  8  4  5   7  7  7  5  7  2  6
129  6  7  7  12  9  7  9 11 NA 11
130 10  5  9   8  8  8  8 10  7 10
131 14 10 12   7 10 11  8  8 11 11
132 11  9 12  14 11 13 12 10 11  9
133  8 11 12  11  8 11 10 12 10  8
134  8 11  8  13 12 11 14 10 17  8
135 11 10  7   8 16 13 10  8 12 12
136 15 16 13  12 16 17 14 12 12 18
137 10 11  7  12  9 11 12 10  9 12
138  7 10  6   7  9  7  6 11  9 12
139 13 16 12   9 14 14 13 10 13 12
140  4  8  5  10  7 10  7 11  4  4
141  7 13 10  11  8 11 10 12 16  9
142 16 19 13  19 14 16 19 19 17 16
143 10  9  5   8 12  8  3 10 11 10
144 10  7  6  12  9  8  9  9  9 12
145 10  6  8  10 12  8  8  5  9 12
146 13 12 10  11  9 10 11 11 12 11
147  2  7  6  13  5  8  5  7  6 10
148  5  7 10   9 11 10 13 10 12 11
149  9 12 10  13  9 12 11  9 11 11
150  6 13  8  13 10 14  9 13 12 13
151 11 10 10  10  6 10 13 11 10  8
152 12  7 13   6  9  6  7 11  7  8
153 15 13  9  13 12 11 11 12 14 13
154  8  7  9   6 11  8  2  6  9  5
155 10  9  9   8  8  7 12 15 10  7
156 11  6  6   6 12  9  6 11  8 11
157  4 10  3   8  4 10  3  5  9  6
158  7 10  6   7 11  7  8  8  5 13
159  7 12  6  11 12 11 11  8  9  8
160  9  9 11   9 14 13 12 12  9 12
161  8  7 10   7  9  5 12  7  9 13
162 10 16  5   9  7 12 10  6 15  8
163 10  9 17  10 14  9  3  7 11 14
164 12 13  8  13  7 13 11 11 10 10
165 11 13 10  13 11 13 12 11 12  9
166  5  7  6   5  9 NA  6  6  5  6
167 10  4  9  12 15  7 10  5  7 13
168 10 10 11  11 12  9  7 11  9 11
169  9  7  6  10 12  7  7 10 10 10
170  8 13 11  11  9 15  9  7 11 11
171  7  9  8  14  7 10  9  9 14 10
172 12  8  9  14  9 11 15  9 12 10
173 12  7 17   8 12 12 13 12  9  7
174 12 10 13  11 12 12 12  8  9 11
175 11 11 10  10  8  8  6  8  9 10
176 11  5  9   7  7  7  7  3  4 10
177 12 12 14  10 11 13 16 13 13 14
178 10 11  9  11 10  8 14 11  9  9
179 14 12 12  10 11 12 13 12  9 15
180  9 13 13  13  9 13 14  6 12 12
181 10  8  8  11 10  7 12 11 11 10
182  9 10 13  13  6 13 13 10  7  6
183 12  3  2   8  9  5  7 12  8  5
184 18 17 12  12 13 16 12 15 12 11
185 12 10  8   8 18 10  9 10  9  9
186 12  9  8  11  8  9  9  9  9 11
187 14 11 11   8  6  9  8  9 10  8
188 12 11 10  14 11 12 13 13 13  8
189 10 13  8   8  5 10  7  6 10  9
190  7 10  7   4  4  5  8  4  8  5
191  8 10 11  11  9  9 10  3 11  7
192 12  6 10  14  8  8  9  5  9 13
193  7 10 10   9  8 10  5 14 11  7
194  9 10 12  11  6 10  9  8 13 11
195  9 10  7  10 12 10  1  7  9  8
196  9 10 12  10  6 11 12 11  9 11
197  8 10  6  11  6  5  8  5 10  9
198 10 10  8  10  9  7 11 12  8 11
199 11 17 13  14  9 14 16  9 11 13
200  8 11 15  14  8 11 15  9  6 14
201  6  6  8   7 10  8 10  7  6  6
202  9  7  5  10  8  4  8  5  6  6
203 13 10 10  11 13 13 10 10 14 11
204 16  9  7  14  9 11  8 16  7 13
205 13 12 10   9  9 12  9 12  7  8
206 10 12 12   8 11 11  8 15 10  7
207 13 13  7  12  7 12  9 10 10 11
208  4  9  6  15  8 11 10 13 11 10
209  9 11  5   7  5 12 10  9 10  6
210  9 11 12  11 11 15  9 10 12 11
211  9  9  5   9  9  7  7  9  7  7
212 10  9  8   9 13 10  8  8 15  2
213 10 14  9  11 10 12 12 10 13 12
214 14 14  9   6 12 12 10  7 13 12
215 10 10  8  11 11 10  9  9  9 10
216 10  9  8   7  7 14  3  7 15 11
217  9 11 14  12 12 13 16  8 14 10
218 17 13 10   8 10 10 12  9 12 11
219  8 12 14  12 11 13 11 12 10  6
220  5  7  8  13 11  9 11  7  8  9
221 12 10  8   9 13 13 10 14 10 16
222 11 13 10   9 12  9 14 12 13 11
223  9  7  6  10  6  7 12  9 11  6
224 13 13  5   8  9  9  6 11  7 14
225 12  9 14   6 12 11 12 13  8 11
226  9 15 12  11  9 13 11 NA 16  8
227  7 14 11   9  7 11 10 12 12 11
228  8 10 13  13 14  7 11 12  8 10
229 10 NA 16  11  8 11 13 15 13 10
230 15 13 14  13 10 13 11 14 17  9
231 12 13 13  12 15  9 12  6 10 12
232  4  1  5   1  7  1  6  6  1  5
233 11 10  8   9 11  9  8  3  8  4
234  9 11 13   7  9  9 12 11 11 12
235 11 13  8  11  9 14 13  7 13  9
236 12  9 12  13 15  7 11 11  8 NA
237  7  7  4   6 10  7  8  3  9  7
238 11 17 14  11 11 13  6 12 10 13
239 NA  8 10   9 11  4  8  5  6 12
240 10  7 14  10 14  8 11 13  9 10
241  9 10 13  11 12  9 10 13  7 14
242  5  2  7   5  7  7  7  7  5  6
243 15 11 10  11  5 12 15 14  8  9
244 13  8 11  11 15  9 11  8  7 13
245  7  9  9  10 10  9 14 12 10 10
246 13 10 10  12 17 12 16 15 16 16
247 15  5 11   9 12  6 11 10  8 13
248  6  9 13  11  4  9 11  9  8  8
249 14 19 19  19 12 17 19 14 17 17
250  8 11 12  12  3 12 11  9  9  6
251  9  7  7   8  5  7  9 11 10  9
252  9  8 14   7  7  7 11  9  8 11
253  2 10  9  15 10 15 11 10 12  9
254  8  7  6   6  7  2  5  6  2  6
255 12 12  5  10  3 11 12 12 10  8
256 10 11  9  16  9 14 13 11 14  8
257 10 11 10  10 14  8 13  6 11  6
258  9  8 10   9 14 11 12 10 13 13
259 12 12  9   9 10 13 10 10 12 12
260 17 17 15  14 17 19 18 19 19 18
261 16 15 11  18 10 17 16 13  9 14
262 11 13 11  11 10 14  9 13 12 NA
263  9  7 12  10  9  8  8  9 10  6
264  5  6  7   9  9  1  8  7  9  8
265 10  6  8   7 10  7  9 10  2  8
266 14 15  8  14 10  9 14 14 12 12
267  3  6 12  10 11  9 11  8 11 NA
268 11 12 10  15  7 17  9 12 16 11
269  7  8 12   8  5 10 12  8  4  8
270 10  8 12  14 14  9 14 12 10 17
271 10 12 14  10  7 12 12 14 11 12
272 11 13 12  10 13 10  8 12  5 12
273  4 11 11   8  7 10  7 11  8 10
274 12 11 10  12 12  5 10  8  6 11
275 13 16 11  12  6  7 12 12  6 10
276  9 10 11  15 14 13 12 13 12 14
277 12  8  5   8 10 10 13 13  6 10
278  8  4  7  12 11  7 12 10 10  6
279  4  7  3   8  4  8  6  7  6  5
280 16 12 13  12  9 11  9 15  9  9
281  6  2  1   7  8  8  2  5  9  6
282 11  9 12  12 13  8 10 10 10 14
283  9 10 11   8  7  9  8 11 15  6
284  7 11  9   6 12  8 11  6 11 16
285 12 11  7  10 10 11  9 14 13 14
286 13 13 11  10 11 13 12 12 12 16
287 13 14 10  14  8 14 10 16 11 11
288 12 12 12  17 11 12  9 11 11 13
289  7  9 13  12  7  5  8 11  8 10
290 10 17  9  16  8 15 13 12 14  9
291 13 13 11  12 10 16 10 10 14 10
292 13 12 12  12  7 12  9  6 12  8
293  9 10  8   7  5  6  8  4  8  7
294 11  8  8   5  9 12 NA 13  6 10
295 10 12  8   5 10 10 10 16  7  9
296  4  7  8   9  9  7 10 11 11  8
297 12 10 11  13 11  9 13 11  9 10
298 10  5  6   8  8  5  9  9  5  5
299  8  6  4  11  7  7  9  7  6  4
300 12 13 11  11  8 16 11 12 12 12
301  1  3  8   5  5  6  6  3  6  3
302  9  6 11   8 10  6 14  9  6 11
303  8  8 10  12  9 10  8  7  9  8
304  2 10 17   9 14 12 13 16  9 11
305 10 11  8  11 15  9  8  8  9 13
306  4 10  6   8 10 10  9  6 13  9
307  6  9 10   5  6  6  5  6  8 16
308 13  9 12   6 13  8 11 10 11 14
309  6 10 12  10  8  8 14  9  6 12
310  9 11 13   9 13  9 12  6  9 13
311 10  8  7   8 11  4 12  6  5 12
312  8  6  9   9 12  6  4  9  9 11
313 14 11 15  11 13 12 12 11 10  9
314 11  7  3   9  7  9  7  8  9 12
315  7  4  4   9  6  8  7 11  8  7
316 13  7  8   8 10  6 10  9 10  7
317  9 14 13  10 11 16 10  9 10 10
318 10  8 11  11 13  6 11 14 13 12
319  8  7  7  11 10  9 10 12  9 12
320 11  8 14  10 12 10 13  9 11 16
321  7  8  8   8 10 10  6  7  8 13
322 11 13  9   6 11 13 11 11 13 10
323 10 11  8   9 13  9  9 13 11 15
324  8  7  4   4  7  7  5  9  5  9
325 11 13 11  11 10 11 16 12 10 14
326  9  6 13  12  9 11 12  7 10 10
327 12 11  9  10  3 12 11 14 10  4
328  8  5 12   7  9  6  7  6  5  5
329 10 14 13  13  9 12 13 15 13 11
330 NA 12 10  12  8 12 12  4  9 10
331 13 13 12   9 11 16 14 14 13 12
332 13 11  7  15 16  7 15 15 10 16
333 12  7 10  10 17  9 10 16 10 18
334  6 15 NA  16  6 13  9 15 12  9
335 13 13  9  13  6 12 13  9 14 11
336 11 11 10  12  6 12 10 11 13 11
337 10  9 15  12 12  8 10  7 11 11
338 12 16 11  15  7 12  9 10 14 10
339  9 11  6  12 10 12  6 13 13  6
340  6  8  8   9 11 14 10 13  9  9
341  9 12  9   7 10  6 10  6 10  7
342 13  9 15  12  7 10 14 13 10  9
343 14 14  5  13 12  7  9 13 10 11
344  8 10  9   8  7 10 10  6  8 10
345 12  8  9   9 15  8  7  8  7  7
346  9 12 14  11  8 13 11 10 15  6
347  8 16 13  11 14 13 10 10 12  7
348  5  8 10  10  6  7 10  8 10  8
349  7  8 11  NA 11 11 12  9 11 13
350  4  2 12  12 13  8 11 12  6  8
351  7  8 11  10  8  9 11  7 13 11
352  9  9  8   9  9 13 10 11 14  8
353  8 10 10  17 14  9 10 11 15 14
354  9 11  9  11  5  7 10 10 14  8
355 13 15 13  11  9 15 13  9 10 12
356  9  8  5   9  5 13 10 13 13  9
357 12 12 12   9 12 10 14 11 11 10
358  8 10  5   6  6  5 10  6  8  8
359 17  9 10   9  9  7  8 13 10 10
360 10 12  9   9 13  9  7 11 11  9
361  8  8  9   9  5 10  9  6  7  7
362 11 12  9  13 11 10 11 15 13  6
363 10 13 15  11 18  8 10 13 11 14
364 10 12  6  12 11  9 12  8 11 13
365 13  2 13   6 10  6  8  6  7 11
366  9 12  5  11  7 11  5 15 NA  9
367 12 10 12   4  3  9  5  9  7  5
368  4  3  5   1 13  1  6  4  4 10
369  8  5  9   9 12  9  7  9  8 14
370 11 15 10  NA 11 12 12  4 11 11
371 12 12  6  13  4 11  6  8 11 12
372  5 11 12  10 10  8  9  5 10  8
373  6  7  5   2  8  5  6 10  4  8
374 10 10  8   9  4 11  9 11 10  6
375 13 11 13  13 12  9  7 11  7 15
376 12  8 11  13 11 14 11 14 13  5
377 13 12 15   8 13 13  8 10 13 15
378  7  7  7   5 13 10  9  9 10  9
379  5 12 14   7  9  8 11 12 10 10
380  7  9 15   9 14  8 12 10 14 15
381 13  6  6  11 13  7  7  8  9 12
382 12 10 15  16 13 12 16 17 10 15
383 12  8  5   7  8 11  7 12  6  4
384  9  7 13   9 10  7 12 10  5 12
385 11 12 11  11  8 15 12 11 11  9
386 10 10 10   8  6  7  8 12  9  9
387 10 12  6  11 13  7 11 10  8 13
388  8 10 12   9 12  9 11  8  7  8
389 13 11 10   8  5 12 11 16 10  8
390 15 11 17  10 13 11  9 11 14  8
391  7 12 12   6  9 13 10  8 10 10
392 16 12 15  14 12 13 14 16 12 14
393 13 11 10   8  9  9 11 12 10 12
394  8  4  7  10  7 11 10  5 10  6
395 12 14 11   6 13 10  9  9  8 11
396 15 11 11   6  9 13 16 11 12 12
397 14 15 14  15 15 13 14 13 14 11
398 12 10  9  12  9 10 12  8  9 12
399 13 11 11  14  8 15  9 15 15  7
400 11 15 13  13  9 17  9 16 17 10

apply family

Here is how you could use the base apply function for computing the mean value by column:

apply(df, MARGIN=2, FUN=mean, na.rm=T)
       BD        SI        DS       PCn        CD        VC        LN        MR 
 9.824121  9.856423  9.706767  9.889169  9.781955  9.867168  9.987437  9.904762 
       CO        SS 
 9.889447 10.005051

In fact, for such a simple task, even colMeans() could be sufficient:

colMeans(df, na.rm=T)
       BD        SI        DS       PCn        CD        VC        LN        MR 
 9.824121  9.856423  9.706767  9.889169  9.781955  9.867168  9.987437  9.904762 
       CO        SS 
 9.889447 10.005051


but let consider slightly more complex cases …

apply family

Let’s say you need to compute the standard deviation per column …

apply(df, MARGIN=2, FUN=sd, na.rm=T)
      BD       SI       DS      PCn       CD       VC       LN       MR 
2.941790 3.137753 3.072283 2.855583 3.022541 3.167819 2.951726 2.989253 
      CO       SS 
2.999217 2.896523


… or to count the number of NA occurrences per column

apply(df, MARGIN=2, FUN=function(x) sum(is.na(x)) )
 BD  SI  DS PCn  CD  VC  LN  MR  CO  SS 
  2   3   1   3   1   1   2   1   2   4

in the latter case, we had to define a custom function, but that’s relatively simple to do!

apply family

Although any of such tasks could be done using a for loop, the code would be more cumbersome and less efficient. For example, here’s how the exact same result as the latter apply example could be obtained using a for loop:

results = rep(NA, ncol(df))
names(results) = colnames(df)

for(i in 1:ncol(df)){
  results[i] = sum(is.na(df[,i]))
}

results
 BD  SI  DS PCn  CD  VC  LN  MR  CO  SS 
  2   3   1   3   1   1   2   1   2   4

apply family

FYI, other functions within the apply family:

  • tapply(): applies a function to subsets of a vector grouped by a factor, example tapply(df$values, df$group, FUN=mean) (know that the function aggregate() might be more convenient in some cases)

  • lapply(): applies a function to each element of a list, returning results in a list format, example lapply(my_list, length)

  • sapply(): the same as the previous one but returns results as a vector if possible, example sapply(my_list, length)

  • mapply() multivariate version of sapply() that runs across more lists or vectors

mapply(rnorm, n=c(2, 6, 4), mean=c(0, 100, 200), sd=c(1, 15, 30))
[[1]]
[1] -0.08178004  2.88841825

[[2]]
[1] 117.59238 108.24465 111.68657  91.52303 101.54431 104.22282

[[3]]
[1] 185.7671 186.2599 215.0463 187.8461

sapply

Here’s how sapply() can be used to help compute the standard error of the mean via Monte Carlo simulation

myList = list()
for(i in 1:10000) myList[[i]] = rnorm(30)

ms = sapply(myList, mean)

sd(ms)
[1] 0.1851159
  1. an empty list is initialized;
  2. a for loop is used to fill each slot in the list with a vector of 30 randomly generated numbers;
  3. sapply is used to compute the mean of each vector in the list;
  4. standard error of the mean is computed as the sd on the vector of the means

Saving all generated data allows for more flexibility in analysis, although it uses more memory

lapply and sapply

Here’s another, even more compact way of doing the same, without using any for loop, but this requires defining a small custom function:

results = lapply(1:10000, function(i) rnorm(30) )

ms = sapply(results, mean)

sd(ms)
[1] 0.1836006


Note: "i" represents the current element of 1:10000 over which lapply iterates. Even though it is practically useless here, because only random numbers are generated at each iteration, it must be included because sapply must pass an alement as the argument to the function by default

Define Custom Functions with function()

Previously, we saw a few cases of custom functions, for example for counting NAs in vectors, or computing the mean of a randomly generated vector

Here is the schema for defining custom functions with input (argument[s]), body, and output (return):

# define new function with some argument(s) as input
myFunctName = function(arg1 = NA, arg2 = NA, arg3 = TRUE){ 
  
  # body, series of operations
    computes several operations 
    variously uses arg1, arg2, arg3 
    get an object named "res" as final result 
 
  # gives an output
  return(res)
}

Define Custom Functions with function()

Here’s a full example:

z_score = function(vect = NA){
  
  vectM = mean(vect, na.rm=T)
  vectSD = sd(vect, na.rm=T)
  z = (vect - vectM) / vectSD
  
  return(z)
}

After creating it, a custom function can be used like any other function:

x = c(101, 90, NA, NA, 114, 87, 106, 98, 93)
z_score(x)
[1]  0.27162785 -0.89033574          NA          NA  1.64485756 -1.20723491
[7]  0.79979313 -0.04527131 -0.57343658

Define Custom Functions with function()

Here’s a slightly more sophisticated example:

z_score = function(vect = NA, naRemove = FALSE){
  
  vectM = mean(vect, na.rm=naRemove)
  vectSD = sd(vect, na.rm=naRemove)
  z = (vect - vectM) / vectSD
  
  return(z)
}

Let’s use it:

x = c(101, 90, NA, NA, 114, 87, 106, 98, 93)
z_score(x)
[1] NA NA NA NA NA NA NA NA NA
z_score(x, naRemove=TRUE)
[1]  0.27162785 -0.89033574          NA          NA  1.64485756 -1.20723491
[7]  0.79979313 -0.04527131 -0.57343658

Define Custom Functions with function()

In some previous examples, custom functions were used directly in combination with apply(), without curly brackets {} or return(), yet they worked!

Why?

Generally, curly brackets {} and return() enhance clarity and are best practice, but in some cases they can be omitted for more compact code:

  • Curly brackets {} can be skipped if all code fits on a single line

  • return() can be omitted if the last (or only) code line represents the output

Define Custom Functions with function()

To clarify the previous slide, these are four alternative and increasingly compact ways of writing the same function:

naCount = function(vect){
  whereNAs = is.na(vect)
  totalNAs = sum(whereNAs)
  return(totalNAs)
}

naCount = function(vect){
  whereNAs = is.na(vect)
  totalNAs = sum(whereNAs)
  totalNAs
}

naCount = function(vect){
  sum(is.na(vect))
}

naCount = function(vect) sum(is.na(vect))